{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T04:06:05Z","timestamp":1771473965598,"version":"3.50.1"},"reference-count":44,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,7,6]],"date-time":"2024-07-06T00:00:00Z","timestamp":1720224000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>A metaheuristic algorithm named the Crystal Structure Algorithm (CrSA), which is inspired by the symmetric arrangement of atoms, molecules, or ions in crystalline minerals, has been used for the accurate modeling of Mono Passivated Emitter and Rear Cell (PERC) WSMD-545 and CS7L-590 MS solar photovoltaic (PV) modules. The suggested algorithm is a concise and parameter-free approach that does not need the identification of any intrinsic parameter during the optimization stage. It is based on crystal structure generation by combining the basis and lattice point. The proposed algorithm is adopted to minimize the sum of the squares of the errors at the maximum power point, as well as the short circuit and open circuit points. Several runs are carried out to examine the V-I characteristics of the PV panels under consideration and the nature of the derived parameters. The parameters generated by the proposed technique offer the lowest error over several executions, indicating that it should be implemented in the present scenario. To validate the performance of the proposed approach, convergence curves of Mono PERC WSMD-545 and CS7L-590 MS PV modules obtained using the CrSA are compared with the convergence curves obtained using the recent optimization algorithms (OAs) in the literature. It has been observed that the proposed approach exhibited the fastest rate of convergence on each of the PV panels.<\/jats:p>","DOI":"10.3390\/a17070297","type":"journal-article","created":{"date-parts":[[2024,7,8]],"date-time":"2024-07-08T07:57:45Z","timestamp":1720425465000},"page":"297","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Crystal Symmetry-Inspired Algorithm for Optimal Design of Contemporary Mono Passivated Emitter and Rear Cell Solar Photovoltaic Modules"],"prefix":"10.3390","volume":"17","author":[{"given":"Ram Ishwar","family":"Vais","sequence":"first","affiliation":[{"name":"Electrical Engineering Department, Rajkiya Engineering College Sonbhadra, Churk 231206, Uttar Pradesh, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5972-1617","authenticated-orcid":false,"given":"Kuldeep","family":"Sahay","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, Institute of Engineering and Technology Lucknow, Lucknow 226021, Uttar Pradesh, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8303-8343","authenticated-orcid":false,"given":"Tirumalasetty","family":"Chiranjeevi","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, Rajkiya Engineering College Sonbhadra, Churk 231206, Uttar Pradesh, India"}]},{"given":"Ramesh","family":"Devarapalli","sequence":"additional","affiliation":[{"name":"Department of Electrical\/Electronics and Instrumentation Engineering, Institute of Chemical Technology, Indianoil Odisha Campus, Bhubaneswar 751013, Orissa, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5741-9548","authenticated-orcid":false,"given":"\u0141ukasz","family":"Knypi\u0144ski","sequence":"additional","affiliation":[{"name":"Faculty of Automatic Control, Robotic and Electrical Engineering, Poznan University of Technology, 60-965 Poznan, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Mahajan, M., Kumar, S., Pant, B., and Khan, R. (2021, January 19\u201320). Improving Accuracy of Air Pollution Prediction by Two Step Outlier Detection. Proceedings of the 2021 International Conference on Advances in Electrical, Computing, Communication and Sustainable Technologies (ICAECT), Bhilai, India.","DOI":"10.1109\/ICAECT49130.2021.9392404"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Bo\u0161njakovi\u0107, M., Santa, R., Crnac, Z., and Bo\u0161njakovi\u0107, T. (2023). Environmental Impact of PV Power Systems. Sustainability, 15.","DOI":"10.20944\/preprints202306.1734.v1"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1625","DOI":"10.1016\/j.rser.2010.11.032","article-title":"A review of solar photovoltaic technologies","volume":"15","author":"Parida","year":"2011","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Sheng, H., Li, C., Wang, H., Yan, Z., Xiong, Y., Cao, Z., and Kuang, Q. (2019). Parameters Extraction of Photovoltaic Models Using an Improved Moth-Flame Optimization. Energies, 12.","DOI":"10.3390\/en12183527"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"110828","DOI":"10.1016\/j.rser.2021.110828","article-title":"A comprehensive survey on meta-heuristic algorithms for parameter extraction of photovoltaic models","volume":"141","author":"Li","year":"2021","journal-title":"Renew. Sustain. Energy Rev."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1818","DOI":"10.3390\/eng4030103","article-title":"Parameter Identification of Solar Photovoltaic Systems Using an Augmented Subtraction-Average-Based Optimizer","volume":"4","author":"Moustafa","year":"2023","journal-title":"Eng"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Ghetas, M., and Elshourbagy, M. (2024). Parameters extraction of photovoltaic models using enhanced generalized normal distribution optimization with neighborhood search. Neural Comput. Applic.","DOI":"10.1007\/s00521-024-09609-x"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"114030","DOI":"10.1016\/j.enconman.2021.114030","article-title":"An improved gaining-sharing knowledge algorithm for parameter extraction of photovoltaic models","volume":"237","author":"Sallam","year":"2021","journal-title":"Energy Convers. Manag."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"594","DOI":"10.1016\/j.solener.2017.01.064","article-title":"Parameters extraction of solar cell models using a modifed simplifed swarm optimization algorithm","volume":"144","author":"Lin","year":"2017","journal-title":"Sol. Energy"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"163379","DOI":"10.1016\/j.ijleo.2019.163379","article-title":"Analytical optimization of photovoltaic output with Lagrange Multiplier Method","volume":"199","author":"Louzazni","year":"2019","journal-title":"Optik"},{"key":"ref_11","first-page":"100423","article-title":"An efficient analytical approach for forecasting the peak power of PV panels working in outdoor conditions based on explicit model","volume":"20","author":"Maouhoub","year":"2023","journal-title":"Energy Convers. Manag."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1016\/j.renene.2016.02.012","article-title":"Analytical and quasi-explicit four arbitrary point method for extraction of solar cell single-diode model parameters","volume":"92","author":"Toledo","year":"2016","journal-title":"Renew. Energy"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"e06673","DOI":"10.1016\/j.heliyon.2021.e06673","article-title":"A combination of Newton-Raphson method and heuristics algorithms for parameter estimation in photovoltaic modules","volume":"7","author":"Gnetchejo","year":"2021","journal-title":"Heliyon"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3026","DOI":"10.1016\/j.solener.2012.07.010","article-title":"Exact analytical solution of a two diode circuit model for organic solar cells showing S-shape using Lambert W-functions","volume":"86","author":"Romero","year":"2012","journal-title":"Sol. Energy"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Ginidi, A., Ghoneim, S.M., Elsayed, A., El-Sehiemy, R., Shaheen, A., and El-Fergany, A. (2021). Gorilla troops optimizer for electrically based single and double-diode models of solar photovoltaic systems. Sustainability, 13.","DOI":"10.3390\/su13169459"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Vais, R.I., Sahay, K., Chiranjeevi, T., Devarapalli, R., and Knypi\u0144ski, \u0141. (2023). Parameter Extraction of Solar Photovoltaic Modules Using a Novel Bio-Inspired Swarm Intelligence Optimisation Algorithm. Sustainability, 15.","DOI":"10.3390\/su15108407"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"9240","DOI":"10.1038\/s41598-023-36284-0","article-title":"Electrical parameters extraction of PV modules using artificial hummingbird optimizer","volume":"13","author":"Shaheen","year":"2023","journal-title":"Sci. Rep."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3979","DOI":"10.1016\/j.egyr.2021.06.064","article-title":"Gradient-based optimization with ranking mechanisms for parameter identifcation of photovoltaic systems","volume":"7","author":"Ahmadianfar","year":"2021","journal-title":"Energy Rep."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"6660115","DOI":"10.1155\/2021\/6660115","article-title":"Enhanced Success History Adaptive DE for Parameter Optimization of Photovoltaic Models","volume":"20212","author":"Song","year":"2021","journal-title":"Complexity"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Yuan, S., Ji, Y., Chen, Y., Liu, X., and Zhang, W. (2023). An Improved Differential Evolution for Parameter Identification of Photovoltaic Models. Sustainability, 15.","DOI":"10.3390\/su151813916"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"113474","DOI":"10.1016\/j.enconman.2020.113474","article-title":"A hybrid adaptive teaching\u2013learning-based optimization and diferential evolution for parameter identifcation of photovoltaic models","volume":"225","author":"Li","year":"2020","journal-title":"Energy Convers. Manag."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"113661","DOI":"10.1016\/j.enconman.2020.113661","article-title":"MPPCEDE: Multi-population parallel co-evolutionary diferential evolution for parameter optimization","volume":"228","author":"Song","year":"2021","journal-title":"Energy Convers. Manag."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"7945","DOI":"10.1038\/s41598-024-58503-y","article-title":"Efficient parameter extraction of photovoltaic models with a novel enhanced prairie dog optimization algorithm","volume":"114","author":"Izci","year":"2024","journal-title":"Sci. Rep."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"164559","DOI":"10.1016\/j.ijleo.2020.164559","article-title":"A new metaphor-less algorithms for the photovoltaic cell parameter estimation","volume":"208","author":"Premkumar","year":"2020","journal-title":"Optik"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"408","DOI":"10.1016\/j.apenergy.2018.06.010","article-title":"Multiple learning backtracking search algorithm for estimating parameters of photovoltaic models","volume":"226","author":"Yu","year":"2018","journal-title":"Appl. Energy"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Wu, H., Chen, Y., Cai, Z., Asghar Heidari, A., Chen, H., and Zhang, Y. (2023). Super-evolutionary mechanism and Nelder-Mead simplex enhanced salp swarm algorithm for photovoltaic model parameter estimation. IET Renew. Power Gener., 1\u201329.","DOI":"10.1049\/rpg2.12973"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1016\/j.renene.2017.04.014","article-title":"Parameter estimation of photovoltaic system using imperialist competitive algorithm","volume":"111","author":"Fathy","year":"2017","journal-title":"Renew. Energy"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Jian, X., and Cao, Y. (2022). A Chaotic Second Order Oscillation JAYA Algorithm for Parameter Extraction of Photovoltaic Models. Photonics, 9.","DOI":"10.3390\/photonics9030131"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/j.ijleo.2017.10.081","article-title":"A novel Elite Opposition-based Jaya algorithm for parameter estimation of photovoltaic cell models","volume":"155","author":"Wang","year":"2018","journal-title":"Optik"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"167973","DOI":"10.1016\/j.ijleo.2021.167973","article-title":"Orthogonal learning-based Gray Wolf Optimizer for identifying the uncertain parameters of various photovoltaic models","volume":"247","author":"Xavier","year":"2021","journal-title":"Optik"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"167977","DOI":"10.1016\/j.ijleo.2021.167977","article-title":"A novel two step method to extract the parameters of the single diode model of Photovoltaic module using experimental Power-Voltage data","volume":"248","author":"Reddy","year":"2021","journal-title":"Optik"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"12282","DOI":"10.1016\/j.egyr.2022.09.069","article-title":"Optimal parameter assessment of Solar Photovoltaic module equivalent circuit using a novel enhanced hybrid GWO-SCA algorithm","volume":"8","author":"Devarapalli","year":"2022","journal-title":"Energy Rep."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Abd El-Mageed, A.A., Al-Hamadi, A., Bakheet, S., and Abd El-Rahiem, A.H. (2024). Hybrid Sparrow Search-Exponential Distribution Optimization with Differential Evolution for Parameter Prediction of Solar Photovoltaic Models. Algorithms, 17.","DOI":"10.3390\/a17010026"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Vandrasi, R.K., Kumar, B.S., and Devarapalli, R. (2022). Solar photovoltaic module parameter extraction using a novel hybrid chimp-sine cosine algorithm,\u201d Energy Sources A: Recover. Util. Environ. Eff., 1\u201320.","DOI":"10.1080\/15567036.2022.2041768"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Gatla, V.R., Injeti, S.K., Kotte, S., Polamarasetty, P.K., Nuvvula, R.S.S., Vardhan, A.S.S., Singh, M., and Khan, B. (2023). An Effective Approach for Extracting the Parameters of Solar PV Models Using the Chaotic War Strategy Optimization Algorithm With Modified Newton Raphson Method. IEEE J. Electron Devices Soc.","DOI":"10.1109\/JEDS.2023.3340445"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Naraharisetti, J.N.L., Devarapalli, R., and Bathina, V. (2020). Parameter extraction of solar photovoltaic module by using a novel hybrid marine predators\u2013success history based adaptive differential evolution algorithm,\u201d Energy Sources A: Recover. Utili. Environ. Eff., 1\u201323.","DOI":"10.1080\/15567036.2020.1806956"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"116025","DOI":"10.1016\/j.energy.2019.116025","article-title":"Optimal parameter identifcation of triple-junction photovoltaic panel based on enhanced moth search algorithm","volume":"188","author":"Fathy","year":"2019","journal-title":"Energy"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"778","DOI":"10.1016\/j.solener.2017.08.084","article-title":"A novel optimal parameters identifcation of triple-junction solar cell based on a recently meta-heuristic water cycle algorithm","volume":"157","author":"Rezk","year":"2017","journal-title":"Sol. Energy"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"13961","DOI":"10.1002\/er.8114","article-title":"Modifed search and rescue optimization algorithm for identifying the optimal parameters of high efciency triple-junction solar cell\/module","volume":"46","author":"Houssein","year":"2022","journal-title":"Int. J. Energy Res."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/4235.585893","article-title":"No free lunch theorems for optimization","volume":"1","author":"Wolpert","year":"1997","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"107904","DOI":"10.1016\/j.cie.2021.107904","article-title":"Improved binary adaptive wind driven optimization algorithm-based dimensionality reduction for supervised classification","volume":"167","author":"Gad","year":"2022","journal-title":"Comput. Ind. Eng."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"71244","DOI":"10.1109\/ACCESS.2021.3079161","article-title":"Crystal Structure Algorithm (CryStAl): A Metaheuristic Optimization Method","volume":"9","author":"Talatahari","year":"2021","journal-title":"IEEE Access"},{"key":"ref_43","unstructured":"(2024, April 25). ARKA_SERIES_WSMD_515_545. Available online: https:\/\/cdn.enfsolar.com\/z\/pp\/g9bqbs274a\/ARKA-SERIES-WSMD-515-545-WEL-E-PD-515-545-144-MP-HC-06-17-11.pdf."},{"key":"ref_44","unstructured":"(2024, June 10). Canadian_Solar_CS7L_MS_575_605. Available online: https:\/\/static.csisolar.com\/wp-content\/uploads\/sites\/2\/2020\/10\/02101505\/Canadian_Solar-Datasheet-CS7L-MS-575-605-V1.6C1_AU.pdf."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/17\/7\/297\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:11:06Z","timestamp":1760109066000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/17\/7\/297"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,6]]},"references-count":44,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2024,7]]}},"alternative-id":["a17070297"],"URL":"https:\/\/doi.org\/10.3390\/a17070297","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7,6]]}}}